"if you think childlike, you'll stay young. If you keep your energy going, and do everything with a little flair, you're gunna stay young. But most people do things without energy, and they atrophy their mind as well as their body. you have to think young, you have to laugh a lot, and you have to have good feelings for everyone in the world, because if you don't, it's going to come inside, your own poison, and it's over" Jerry Lewis
"I don’t believe
in the irreversibility of situations" Deleuze

Note on Citations

The numerical citations refer to page number. The source's text-space (including footnote region) is divided into four equal portions, a, b, c, d. If the citation is found in one such section, then for example it would be cited p.15c. If the cited text lies at a boundary, then it would be for example p.16cd. If it spans from one section to another, it is rendered either for example p.15a.d or p.15a-d. If it goes from a 'd' section and/or arrives at an 'a' section, the letters are omitted: p.15-16.

[Note: All boldface and underlining is my own. It is intended for skimming purposes. Bracketed comments are also my own explanations or interpretations.]

Henry Somers-Hall

Hegel, Deleuze, and the Critique of Representation.

Dialectics of Negation and Difference

Part 1: The Problem of Representation

Chapter 2: Difference and Identity

Subdivision 2: Aristotle

Brief Summary:

We are seeking the transcendental field in Deleuze, which would be the genetic production of individuals [which we might mentally grasp], and for Deleuze this transcendental field is immanent in empirical givenness. One possibility is Aristotle’s concept of species’ difference (specific difference), because it also is genetic. Aristotle categorizes things under three main tier-relations: genus, species, and individual. For example, Animal, Man, Socrates. But animal is also a species of a higher genus, and so on up to the highest genus [, being]. For Aristotle, there is a specific difference that distinguishes one species from another [and thus from the genus itself taken in its generality and not in terms of its internal heterogeneity]. This specific difference does not tell us something accidental about the species but rather something necessary and essential. So man is a rational animal. Because the specific difference is essential to the species, it is inherent to it, and thus it is productive of its differences from the other species in it genus. For, it is not that the genus is divided into things that on account of this division obtain their differences, because the differences were already inherent to the species. Thus the specific differences are what produce the various species in the genus, [and the genus is merely the general category resulting from grouping the species according to what is commonly reducible in all the species.] However, there is a problem with consistency if we were to take species difference as productive of all differences constituting the things we might mentally grasp, because it does not explain the differences between individuals for example, which may be distinguished by inessential accidental traits.

Summary

Aristotle founded the systematic study of logic, namely, syllogistic logic. Rather than examine syllogistic logic, Somers-Hall (SH) will focus on “the system of organization of genera, species, and individuals which underlies this syllogistic reasoning”. (43) “For Aristotle, the terms operated on by logic have an essentially hierarchical organization, with the lowest term, the individual, being subsumed under an intermediate term, the species, which is itself subsumed under a genus.” (43) Things fall under a genus. When we define these things falling under the genus, the genus itself is a part of that definition, which means that the genus is essential to what is predicated of it. Now consider the genus animal. Socrates is an animal, so the genus animal is predicated of the individual Socrates. [Now consider if each individual of a genus were only definable with that genus and thus having nothing to distinguish one member of the genus from the others. This would mean that there is only a difference in number and not in kind of each member.]

The genus is "what is predicated in [the category of essence] of a number of things exhibiting differences in kind." What this means is that the genus is a part of the definition of whatever falls under it, that is, it is essential to those things of which it is predicated. The second part of this statement refers to that of which the genus is predicated. While it is the case that for a given genus, say, animal, it is predicated of an individual, for instance Socrates, since it is clear that Socrates is an animal, the reference to a difference in kind in Aristotle's definition means that there must be an intermediary between the genus (animal) and the individual (Socrates). This is because if the genus were related directly to the individual, the genus would be the only function that was essential to each individual. This would mean that in essence each individual would be different only in number, whereas the definition of genus requires that what it is predicated of also differs in kind. (43)

So in between each genus and individual is an intermediary, which is the species, “ ‘that which is predicated of many things which differ in number’ (ISA, 35)”. So Socrates is both a man (species) and an animal (genus). Animal is included in the genus substance, which would then make animal now seem like a genus in relation to man but a species in relation to substance.

Thus we now have a hierarchy, reaching from the highest genera to the individual, through which the individual is specified by a process of division from the genus through the various species, gaining determinations as it goes, since each genus will determine the essence of that below it. (44)

This is the first theory of classes.

What is key to recognize in this theory of classes is that it makes possible the definition of the lowest species purely in terms of universals. From the highest genus, we can move through a process of division, whereby at each stage there is a branching of the higher concept into multiple options, allowing the particular entity to be more and more closely specified. Thus Socrates is the final point of an arborescent structure, characterized by a perpetual process of branching in terms of universal properties. (44)

In Aristotle’s system, the universal performs two functions.

[1] The universal “provides the necessary linguistic economy to allow an infinite number of things to be described using a purely finite number of terms.” (44)

[2] The universal allow mirrors structures in the world, which allows logic to match up with the world. “As Aristotle believes that we can truly talk about things within the world, it must be the case that terms such as properties, which have universal application, can find a place within the world. Thus, for Aristotle, the genera and species pick out real features of the world.” (44) But there is a problem with Aristotle’s system. The species and genera need to group things according to criteria that capture something common “to their essence.” (45) So Aristotle distinguishes homonymy, synonymy, and paronymy.

[1]Homonymy [equivocity]: things are homonymous when they have a name in common but the definition differs. For example a man and a picture of an animal can both be called an animal [in our conversations about the man or the image in the picture], but we would need a different definition for each one [since they are not both animals in the same sense, as one is a pictoral representation of one]

[2]Synonymy [univocity]: things are synonymous when both their name and their definition is the same. Consider for example how both man and ox are animals. [Insofar as we define both strictly as animal, both their name and definition would be the same.]

[3]Paronymy [derivativity]: things are paronymous when they derive their name from a common source but their endings differ. For example, grammarian and grammar, brave and bravery. (45)

Consider for example homonymity. The term animal can refer both to a man and to a picture of a man. So we group two things that should be differentiated. Thus when we define ‘animal’, we are “forced into a definition of a species that does not accurately capture what it is to be that particular thing” (45). Thus “What is important in these definitions is the recognition that certain forms of differentiation of species may not capture what is essential to the species itself.” (45) In fact, there will always be some degree of homonymity, so “much of Aristotle 's logical work consists in a struggle against the possible encroachment of homonymy within the logical system.” (45)

Defining terms in Aristotle’s hierarchical model:

A definition contains the genus (because the genus is predicated of the species), so for example the definition of man includes ‘animal.’

to the species will be attributed a difference that allows it to differ both from the genus and from other species that are subsumed under the genus. Thus, the species to which man belongs is a species of animal characterized by its rationality. Man therefore becomes a rational animal. (46)

And because of the hierarchical model, ‘animal’ is further differentiated from other species under its genus, ‘substance.’ These tiers of differentiation allow us to specify the essence of what is under definition.

Man is defined by the combination of its genus with a difference, the animal that is rational, and the genus is defined similarly, hence animal is further clarified as the substance with animality. Thus man is specified through rationality, animality, and substance. The concept of difference plays an important role, therefore, as difference in kind is essential to Aristotle's system. (46)

Hence what distinguishes one species from the others in its genius is some specific difference that captures the essence of that species. So consider the designation man is a rational animal. All the other animals are not rational. We might also think of this designation as indicating the species’ difference from the genus, because the genus does not have ‘rational’ in its essence. The genus ‘animal’ has some other essential trait that distinguishes it from other substances. But in order for it to be essential, the specific difference cannot be accidental. (46) For this purpose, Aristotle introduces some other concepts, one being property. A property is something that can identify what species an individual belongs to. It is a trait that appears in one species [but not in the others in its genus, supposing that is what ‘derivative species’ are (46).] However, not every individual in the species will necessarily have this property and [so it is for this reason that] they do not define the thing’s essence. [[There are four types of properties. [1] traits found in only one species, but not necessarily in every member of that species, for example, ‘to heal’ or ‘to geometrize’ in man. [2] traits found in all members of a species but are found in other species as well, for example, ‘being a biped’ in man is also in other animals. [3] traits that happen to all members of a species at a certain time, for example turning grey in man. [4] traits that are found only in one species and in all members of that species, for example risibility in man. What will seem to make the important distinction between properties and accidents is that at least some in a species needs to have a property proper to it, where no members of a species need to have an accident.]

a property differs from the kind of difference we have been talking about in that it only occurs within a particular species (although not every individual within a particular species needs to exhibit it), rather than also occurring in derivative species. Examples of properties include "the capacity to laugh in man" or "becoming grey in old age" (ISA, 48) . These properties do not define the essence of a particular thing, although they do, at least in the first case, extensionally define a species so that that which can neigh is a horse, and a horse is that which can neigh. (46)

An accident on the other hand only gives us a trait which need not be found in any member of a species, but very well could or even very commonly is found in them.

Accidents, though similar to properties, "come into being and pass away apart from the substratum" so that "it is possible to conceive of a white crow and of an Ethiopian who has lost his colour apart from the destruction of the substratum" (ISA, 49). (46)

True Aristotelian difference is different from properties and accidents. A property need not be found in all members of a species, and an accident can be removed without destroying the species. However “True Aristotelian difference therefore differs from properties in that it applies to all derivative species and from accidents in that it cannot be removed from a subject without that subject's destruction.” (46) Aristotle uses the concept of difference in three ways.

[1] Common difference. [Because of diversity of nature, something differs from another thing by being diversely different from it, and something differs from itself over time in that it diversifies from itself.] “First, common difference defines difference as commonly understood-that is, difference in any way, as, for instance, Socrates differs from Plato ( ISA, 42)”. (46d)

[2] Proper difference. [Two things might be differentiatable but connected by an inseparable accident. For example, a wound always has blueness (or a wound’s blueness is inseparable from it)] “Proper difference is difference in terms of an accident.” (47a)

[3]Specific difference. It is a trait that distinguishes one species from another.

“Therefore while the first two lead to a difference in quality, the third leads to a difference in essence.” (47a)

Thus we see the role of difference in Aristotle’s system.

We have now designated the features of Aristotle's system central to our account of Deleuze's argument. Aristotle's system provides a hierarchical arborescent structure through which the essence of a species can be specified through a process of division, from the most general to the specific. Central to this hierarchy is the concept of difference. It is difference that differentiates the different species from the genera, through this process of division. (47)

Deleuze will critique Aristotle’s concept of difference.

Genus, species, and individual are the three levels in Aristotle’s system. Some sort of a difference will be responsible for generating the hierarchy of terms. But it cannot be the differences found between either individuals or genuses. [Consider the differences that distinguish one man from another. One is tall and the other short. One has brown hair the other blond. None of these differences are essential to being human. They are all accidental.] So difference at the level of the individual is accidental, which “will not capture this essence, instead merely reflecting the 'accidental' deviation from the proper form which the essence will exhibit within the particular individual.” (47) [However, consider things that differ in genus, like animals and minerals.The difference between them is so great that they are incomparable. The differences between individuals is too small for comparison. But] The difference between species, specific difference, then provides the greatest difference. “That is, difference between genera can also not be definitive for Aristotle, as the difference between genera cannot define their difference in terms of a higher, common source. Therefore specific difference becomes the greatest difference for Aristotle” (47)

Recall how in the first chapter,

Deleuze's ontology moves away from a Kantian conception of the transcendental by trying to consider the transcendental as generative, as opposed to merely conditioning. Aristotle's conception of difference at first seems to fulfill the criteria of a properly productive concept, which would allow this ideal to be realized (DR, 31). [47]

For Aristotle, a thing’s essence is a formal characteristic of it. [Recall how specific difference is what determines the essential differences between species. So] for Deleuze, specific difference is generative of essence in Aristotle, and it is a formal characteristic of a thing and as such presents itself as a pure difference. And specific difference, unlike the differences between individuals, “also has a qualitative characteristic, as it defines differences in kind, rather than numerical differences” (48a). Deleuze as well finds Aristotle’s specific difference to be productive and synthetic. The species is composed of both a specific difference [from the others in its genus and thus from the genus itself, taken in its generality] and the genus. Because it is composed of both difference and genus, it is synthetic. And as we saw, the difference is a part of the essence; [it is in the essence of the thing to have its particular difference, thus] the species difference is what is doing the dividing of the genus, rather than the genus being divided into what are then differences as a result of the division. (48a) So difference “plays an active role in defining the species”. (48)

Difference thus has all of the characteristics that were attributed to the concept of difference that Deleuze himself employs, the difference that was outlined in the first chapter. Without the concept of difference, it would be impossible to move from the highest genus to any of its intermediaries. Aristotle's concept of difference is thus, like Deleuze's, directly responsible for the generation of the individual. Division thus appears as differenciation. (48)

Yet, there are still problems with assimilating Aristotle’s species difference with Deleuze’s difference.

[1] Aristotle’s difference is parasitic on a higher identity, because you cannot have a species difference without that species also belonging to a genus. “genera are logically prior to differences and are not logically dependant on them, whereas differences are logically dependant on genera ( that within which they are a difference)” (48)

[2] It is unclear how difference would produce the essence of the highest genus. “The highest genera form the top of the hierarchy of species, from which the species are differenciated by difference. This highest point in the hierarchy, however, cannot itself be the result of differentiation, as, if it was, this would presuppose a higher genus, from which this genus would itself be divided. Given that species and their differentiae are reliant on the preceding genus, the question of the status of difference at the top of the hierarchy now becomes problematic.” (48)

[3] Individuals are distinguished by their differences but they are not the essential differences of species differences. “A similar problem arises at the lowest point, where we have the problem of common difference. To quote Porphyry once again, "[C]ommonly one thing is said to differ from another when by otherness it differs in any way at all from either itself, or from another, for by otherness, Socrates differs from Plato and, indeed, from himself: he was a child and became a man" (ISA, 42) . The second problem is to explain in this Aristotelian system how Socrates can differ from himself and yet remain under the identity of the same concept, given that differentiation takes place in relation to the species and essence, through Aristotle 's focus on specific difference, and not in relation to the individual, which is understood through the contingencies of accidental difference.” (48) We have the problem then of knowing how to differentiate accidental from essential properties in the individual.

SH concludes by leading us into the next chapter section:

Aristotle's concept of difference therefore seems to be problematic on both sides. As Deleuze | puts it, "[S]pecific difference refers only to an entirely relative maximum, a point of accommodation for the Greek eye which sees the mean, and has lost the sense of Dionysian transports and metamorphoses" (DR, 32) . The failure to find a truly Deleuzian concept of difference in Aristotle's logic may be indicative of problems, but it is not in its own right problematic itself. We therefore need to look at these two problems in further detail, that of the genus, and that of the individual. (48-49)